65 problems

Let $(X,D)$ be a log Calabi–Yau surface pair with $D=D_1+\cdots+D_l$, and define … where $\mu$ is the Möbius function. Klemm–Pandharipande integrality conjecture. When $l=2$, the q…

Let $X$ be a polarized Calabi–Yau $3$-fold, let $\overline{\Omega}_\gamma^X\in\mathbb{Q}$ be its Donaldson–Thomas invariant, and define the BPS invariant…

Let $\mathcal L$ be an $r$-component link, with components colored by representations $R_1,\ldots,R_r$, and let $f_{(R_1,R_2,\ldots,R_r)}(q,\lambda)$ denote its reformulated invari…

Relative BPS integrality conjecture. For every $d\geq 1$,

Let $E\subset X$ be a super-rigid elliptic curve, and let $N_g(n\cdot E)$ denote the genus-$g$ Gromov–Witten invariant in the class $n\cdot E$. Gopakumar–Vafa local elliptic-curve…

Let $X$ be the Calabi–Yau threefold considered above, let $\beta\in H_2(X,\mathbb Z)$, and let … be the surjective morphism from the normalization of the sheaf moduli space to the…

Global Stokes transformation–BPS spectrum-generator conjecture. The global Stokes transformation can be identified with the spectrum generator of BPS invariants.

Stokes–BPS correspondence. The Stokes constants of the topological string free energy can be identified with the BPS invariants of the associated four-dimensional theory.

Let $C$ be an integral projective locally planar curve over $\mathbf{k} = \mathbb{C}$, let $g=g(C)$ and $\widetilde{g}=\widetilde{g}(C)$ be its arithmetic and geometric genera, and…

Let $(C,0)$ be a reduced planar curve singularity over $\mathbf{k} = \mathbb{C}$, let $\delta$ be its $\delta$-invariant, and let $n_h(C,0)$, $0\leq h\leq\delta$, be the BPS invari…

Let $X$ be a Calabi–Yau 3-fold, and let its BPS invariants and Gromov–Witten invariants be the enumerative invariants associated with $X$. BPS/Gromov–Witten invariants equivalence…

Let $A$ be the contraction algebra of a rational flopping curve $C$, namely a Jacobi algebra of the type defined in the cited work. For every $d\in\mathbb{N}$, let…

Let $S$ be a smooth projective surface, let $\beta\in H_2(S,\mathbb{Z})$ satisfy … and let $K_S$ be the total space of the canonical line bundle over $S$, viewed as a non-compact C…

Let $S_n$ be the blow-up of $\mathbb{P}^2$ at $n$ general real points, and let $\beta\in H_2(S_n,\mathbb{Z})$ be a curve class such that … Here $BPS_\beta^{S_n}(q)$ denotes the BPS…

Consider a type II$_{b}$ limit associated with a Tyurin degeneration of the form $V_0=V_1\cup_Z V_2$ and a special Lagrangian 3-cycle $\Gamma_0$ dual to an element of…

Let $\mathcal{L}^{\vec{\tau}}$ be a framed $L$-component link, and let $p_{r_1,\ldots,r_L}(\mathcal{L}^{\vec{\tau}};q,a)$ be the Laurent polynomial appearing after factoring…

Let $\mathcal{L}^{\vec{\tau}}$ be a framed $L$-component link with component framings $\vec{\tau}=(\tau_1,\ldots,\tau_L)$. For nonnegative integers $r_1,\ldots,r_L$, not all zero,…

Stokes-constant/BPS-invariant conjecture. These Stokes constants are given by BPS invariants.

Parametric resurgence–BPS conjecture. The “parametric” resurgent structure of topological strings on Calabi–Yau threefolds is closely related to the spectrum of BPS states and to B…

Let $X$ be a local Calabi--Yau threefold in an integral frame, and let $\underline{r}$ be an integer-valued vector satisfying the leading vanishing blowup equation … Among such vec…

Canonical BPS integrality conjecture. For this choice of mixed Hodge structure, there is an isomorphism as in the cohomological integrality conjecture. This strengthens the precedi…

Let $\mathcal{C}$ be a 3-Calabi–Yau Abelian category on which the Euler form vanishes, and let…

Let $\mathcal{A}$ be a fixed 2-Calabi–Yau category, let $\mathfrak{M}_{\mathcal{A}}$ be its stack of objects, and let $\operatorname{K}(\mathcal{A})$ be its Grothendieck group. For…

Let $(Q,W)$ be a quiver with potential associated to a non-compact Calabi–Yau threefold, let $\Gamma$ be its charge lattice, and let $\langle-,-\rangle$ be the antisymmetrized Eule…

Let $\Gamma$ be the charge lattice, let $\Pi$ be a slice of the complexified Kähler moduli space, and let $\gamma\in\Gamma$ and $z\in\Pi$. An attractor flow tree is a finite decora…